SAND and GRAVEL Ltd has been contracted to provide top soil for three residential housing developments. Top soil can be supplied from three different sites as follows: Weekly capacity Site (Cubic metres) A 100 B 200 C 200 Demand for top soil generated by the construction project is as follows: Weekly Capacity Project (Cubic metres) 1 50 2 150 3 300 The general manager of SAND and GRAVEL Ltd has estimated the cost per cubic metre to transport to each of the possible routs as follows: Cost ($) per Cubic metre to From Project 1 Project 2 Project 3 A $4 $2 $8 B 5 1 9 C 7 6 3 (a) Determine the initial basic transportation schedule and its cost using the (i) North – West Corner Method (ii) Least – Cost Method (iii) Vogel Approximation Method (b) Using the stepping – stone method find the optimum transportation schedule and the cost.